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  "body": "\n## Summary\n\nThe discrete Poisson equation $\\Delta u = f$ asks for a function on a grid or graph whose [[discrete Laplacian|ZN30Y1ZDB6]] is a given function $f$.\nIt is the finite difference version of Poisson's equation $\\Delta u = f$, and with $f = 0$ it becomes the discrete form of [[Laplace's equation|S8RG6N1PRT]].\nWith boundary values prescribed, it becomes a large sparse linear system.\nSolving this system fast is a central task of numerical analysis, done with iterative methods, multigrid or the fast Fourier transform.\n\n## Explanations\n\n### L1 human\n\nLay a square grid over a metal plate and keep the edges at fixed temperatures.\nInside, each grid value should equal the average of its four neighbours, corrected by a heat source term.\nWriting this rule at every inner point gives one linear equation per point.\nSolving all of them at once gives the temperature at every grid point.\n",
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